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Estimation of comparable standardized mean differences in cluster randomized trials with covariate adjustment
Journal article   Open access   Peer reviewed

Estimation of comparable standardized mean differences in cluster randomized trials with covariate adjustment

Juyoung Jung, Zhijiang Liu and Ariel M Aloe
British journal of mathematical & statistical psychology
07/15/2026
DOI: 10.1111/bmsp.70062
PMID: 42454368
Appears in  UI Libraries Support Open Access
url
https://doi.org/10.1111/bmsp.70062View
Published (Version of record) Open Access

Abstract

Standardized mean differences (SMDs) are widely used to quantify treatment effects in cluster-randomized trials. However, covariate adjustment in hierarchical linear models reduces the residual variance components used for standardization, which artificially inflates effect size estimates and undermines comparability across studies. We propose a unified family of estimators that recover the unadjusted variance components by rescaling the covariate-adjusted variance components using pseudo- indices. This rescaling places effect size estimates on a common reference scale, thereby improving comparability across studies and model specifications under standard modeling assumptions. The framework accommodates three covariate adjustment scenarios including level-1, level-2, and simultaneous both-level adjustments. Furthermore, it introduces three estimator types spanning method of moments, maximum likelihood, and a t-statistic reformulation suitable for meta-analysis from published summaries, alongside delta-method variance approximations for each. An empirical example and a simulation study apply the proposed covariate-adjusted SMDs across these scenarios to illustrate their implementation and demonstrate the consequences of omitting the correction.
 covariate adjustment meta‐analysis hierarchical linear models cluster‐randomized trials standardized mean differences UIOWA OA Agreement

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